Abstract
A finite-difference time-domain (FDTD) method based on a regular Cartesian Yee's lattice is developed for
calculating the dispersion band diagram of a 2-D photonic crystal. Unlike methods that require auxiliary difference
equations or nonorthogonal grid schemes, our method uses the standard central-difference equations and can be easily
implemented in a parallel computing environment. The application of the periodic boundary condition on an angled
boundary involves a split-field formulation of Maxwell's equations. We show that the method can be applied for
photonic crystals of both orthogonal and nonorthogonal unit cells. Complete and accurate bandgap information is
obtained by using this FDTD approach. Numerical results for 2-D TE/TM modes in triangular lattice photonic crystals
are in excellent agreement with the results from 2-D plane wave expansion method. For a triangular lattice photonic
crystal slab, the dispersion relation is calculated by a 3-D FDTD method similarly formulated. The result agrees
well with the 3-D finite-element method solution. The calculations also show that the 2-D simulation using an
effective index approximation can result in considerable error for higher bands.
© 2007 IEEE
PDF Article
More Like This
Cited By
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
Contact your librarian or system administrator
or
Login to access Optica Member Subscription